document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117767>Question 117767</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many two-letter permutations can be made from the letters L,M,N,O, and P? \r<BR>\n" );
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document.write( "How many three-letter combinations can be made from the letters in the word BLACK?\r<BR>\n" );
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document.write( "Thanks whoever helps me because I am totally confused. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85743 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85743\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to show you 2 ways you can tackle these types of problems\r<BR>\n" );
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document.write( "Method #1:\r<BR>\n" );
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document.write( "Since 2 only places to put them, you can visualize of the problem as a series of slots like this:\r<BR>\n" );
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document.write( "Now since you have 5 distinct letters, you have 5 choices for the first slot. Once you take away one letter, you are left with 4 letters. So you'll have 4 choices for the 2nd slot. Now simply multiply these two numbers to get\r<BR>\n" );
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document.write( "5*4=20\r<BR>\n" );
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document.write( "So you'll have 20 unique combinations\r<BR>\n" );
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document.write( "Method #2:\r<BR>\n" );
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document.write( "Since we're talking about permutations, we can use the permutations formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}P_{r}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-r%29%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-r%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}P_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%21%2F%285-2%29%21 ALIGN=MIDDLE  ALT=\"5%21%2F%285-2%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=5 ALIGN=MIDDLE  ALT=\"n=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the total number of letters that you have) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2 ALIGN=MIDDLE  ALT=\"r=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the number of letters that you can use at one time) note: the value of n is greater than r. In other words n>r.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}P_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%21%2F3%21 ALIGN=MIDDLE  ALT=\"5%21%2F3%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-2 ALIGN=MIDDLE  ALT=\"5-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 3\r<BR>\n" );
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document.write( "Expand 5!<BR>\n" );
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document.write( "Expand 3!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}P_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%2A3%2A2%2A1%29%2F%283%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%285%2A4%2A3%2A2%2A1%29%2F%283%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}P_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%2Across%283%2A2%2A1%29%29%2F%28cross%283%2A2%2A1%29%29 ALIGN=MIDDLE  ALT=\"%285%2A4%2Across%283%2A2%2A1%29%29%2F%28cross%283%2A2%2A1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Cancel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}P_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A4 ALIGN=MIDDLE  ALT=\"5%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{5}P_{2}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Now multiply 5*4 to get 20\r<BR>\n" );
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document.write( "So 5 choose 2 (where order does matter) yields 20 unique combinations\r<BR>\n" );
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document.write( "---------\r<BR>\n" );
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document.write( "So no matter what method you choose, you'll get the same answer. </SPAN>\n" );
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